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Balanced picture fuzzy graph with application

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Abstract

Picture fuzzy graphs are an extension of intuitionistic fuzzy graphs. Balanced picture fuzzy graph is a special type of picture fuzzy graph (PFG). In this study, the definition and important properties of PFG like, average PFG, balanced PFG, size, order, density of a PFG, isomorphism, the direct product of two PFG, etc have been studied. The necessary and sufficient conditions for balanced picture fuzzy graphs have also been studied in this article. Beside this, we proposed an algorithm to test whether a PFG is balanced or not. The proof of correctness and an illustration of the proposed algorithm is presented in this article. Lastly, an application of balanced PFG to business alliance is presented.

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Acknowledgements

We would like to thank the anonymous reviewers for their insightful and constructive comments and suggestions that have been helpful for providing a better version of the present work.

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Authors and Affiliations

  1. Department of Mathematics, Raghunathpur College, Raghunathpur, Purulia, 723121, India

    Sk Amanathulla

  2. Department of Mathematics, Kabi Jagadram Roy Government General Degree college, Mejia, Bankura, 722143, India

    Biswajit Bera

  3. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Madhumangal Pal

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  1. Sk Amanathulla
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  2. Biswajit Bera
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  3. Madhumangal Pal
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Correspondence to Biswajit Bera.

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Amanathulla, S., Bera, B. & Pal, M. Balanced picture fuzzy graph with application. Artif Intell Rev 54, 5255–5281 (2021). https://doi.org/10.1007/s10462-021-10020-4

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